Water boils in an electric kettle in 15 minutes after switching on. If the length of the heating wire is decreased to `2//3` of its initial value, then the same amount of water will with the supply voltage in

Options

A. 15 minute
B. 12 minute
C. 10 minute
D. 8 minute

Answer

C

Explanation

(c ) `H = (V^(2))/(R ) t`
Since supply voltage is same and equal amount of heat will produce, therefore
`(R_(1))/(t_(1)) = (R_(2))/(t_(2))` or `(R_(1))/(R_(2)) = (t_(1))/(t_(2))`
But `R prop l implies (R_(1))/(R_(2)) = (l_(1))/(l_(2))`
By (i) and (ii), `(l_(1))/(l_(2)) = (t_(1))/(t_(2))`
Now `l_(2) = (2)/(3) l_(1) implies (l_(1))/(l_(2)) = (3)/(2)`
`:.` By equiation (iii), `(3)/(2) = (15)/(t_(2)) implies t_(2) = 10` minutes